Non-equilibrium relaxation in a stochastic lattice Lotka–Volterra model

Chen, Sheng; Täuber, Uwe C.

doi:10.1088/1478-3975/13/2/025005

Non-equilibrium relaxation in a stochastic lattice Lotka–Volterra model

Journal Article · Tue Apr 19 00:00:00 EDT 2016 · Physical Biology (Online)

DOI:https://doi.org/10.1088/1478-3975/13/2/025005· OSTI ID:1855165

Chen, Sheng ^[1]; Täuber, Uwe C. ^[2]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Virginia Tech, Department of Physics
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

We employ Monte Carlo simulations to study a stochastic Lotka–Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. Here, the numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold.

View Accepted Manuscript (DOE)

Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0002308

OSTI ID:: 1855165

Alternate ID(s):: OSTI ID: 22758436

Journal Information:: Physical Biology (Online), Journal Name: Physical Biology (Online) Journal Issue: 2 Vol. 13; ISSN 1478-3975

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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59 BASIC BIOLOGICAL SCIENCES
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